Streak's claims that Zimbabwe's selectors were discriminating against white players, which led to him being sacked as captain in April and provoked 15 rebels to walk out.
"I don't think other countries should be playing Test or One-day cricket against Zimbabwe until the current crisis has been resolved," he told the Daily Telegraph.
"It's a difficult one for the ICC, but they may have to force the two parties involved to talk and to try to come up with some sort of resolution.
"I hope that the damage can be repaired.
"But there is increasing polarisation between the two parties, and the longer it goes on the more difficult it's going to be to get an agreement."
Streak, who has decided to move to England to play for Warwickshire, insisted his demand for an international ban was based on cricketing rather than political reasons.
"Players are being discriminated against because they are white, which is the main problem," he said.
"But it isn't a purely black and white thing. There's also regional discrimination as well."
Streak had already decided to play County cricket before falling out with the ZCU but he now fears his international career is over.
"I hope that my Zimbabwe career isn't finished. But, in my heart of hearts, it's difficult to see how I can play again unless the ICC get involved."
Zimbabwe's future as a Test team will be discussed when cricket chiefs from India, South Africa and Australia meet ZCU boss Peter Chingoka in Dubai on Thursday.
Sources say the Dubai discussions about the on-going crisis will form the basis for a final decision on Zimbabwe's future at the ICC's annual conference in June.
England are due to tour Zimbabwe in October but last month's Test series with Australia was suspended after Zimbabwe were humiliated by Sri Lanka.